Rotational Motion - Theory & Concepts - Rotational Kinematics

A comprehensive overview of Rotational Motion explaining angular kinematics, dynamics, energy, and momentum.

Interactive engineering simulation

Study the motion of a particle rotating on a disk. Observe how physical tangential and centripetal acceleration vector components scale at radius R.

Initial Velocity (ω0)3.0 rad/s

rad/s

-8.0–8.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Angular Acceleration (α)0.8 rad/s²

rad/s²

-4.0–4.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Tracking Point Radius (R)1.5 m

0.5–2.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Time Elapsed (t)4.0 s

0.0–10.0

Drag for exploration or enter an exact value. Press Enter to apply; Escape restores the current value.

Constant Acceleration Formulas

Final Velocity:

\omega = \omega_0 + \alpha t

Displacement:

\theta = \omega_0 t + \frac{1}{2}\alpha t^2

Linear Vector Magnitudes:

a_c = \omega^2 R

a_t = \alpha R

Note that centripetal acceleration increases with the square of speed, while tangential acceleration remains constant under constant $\alpha$.

Angular Velocity (ω)

6.20 rad/s

Angular displacement (θ)

18.40 rad

Centripetal Accel. (ac)

57.66 m/s²

Tangential Accel. (at)

1.20 m/s²

Model scope and verification

Use the displayed units and idealizations, then verify the governing balance or compatibility equation before interpreting the result.

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